A Schröder-Bernstein theorem in Baer$^{\ast }$-rings with lattice-theoretic proof
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- by Jôsuke Hakeda PDF
- Proc. Amer. Math. Soc. 76 (1979), 131-132 Request permission
Abstract:
The Schröder-Bernstein theorem (SB-theorem) for $*$-equivalence of projections of a $\mathrm {Baer}^*$-ring is known. Here, we will prove an SB-theorem for algebraic equivalence (Theorem A) as a consequence of a lattice-theoretic SB-theorem (Theorem B). Theorem A and the known result about $*$-equivalence will be derived from Theorem B.References
- S. K. Berberian, On the projection geometry of a finite $AW^*$-algebra, Trans. Amer. Math. Soc. 83 (1956), 493–509. MR 85482, DOI 10.1090/S0002-9947-1956-0085482-8 —, $Bae{r^ \ast }$-rings, Springer-Verlag, Berlin, 1972.
- Irving Kaplansky, Rings of operators, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0244778
- Arnold Lebow, A Schroeder-Bernstein theorem for projections, Proc. Amer. Math. Soc. 19 (1968), 144–145. MR 219455, DOI 10.1090/S0002-9939-1968-0219455-2
- F. Maeda and S. Maeda, Theory of symmetric lattices, Die Grundlehren der mathematischen Wissenschaften, Band 173, Springer-Verlag, New York-Berlin, 1970. MR 0282889, DOI 10.1007/978-3-642-46248-1
- Shûichirô Maeda, On the lattice of projections of a Baer $^*$-ring, J. Sci. Hiroshima Univ. Ser. A 22 (1958), 75–88 (1958). MR 105378
- Alfred Tarski, A lattice-theoretical fixpoint theorem and its applications, Pacific J. Math. 5 (1955), 285–309. MR 74376, DOI 10.2140/pjm.1955.5.285
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 76 (1979), 131-132
- MSC: Primary 06A23; Secondary 16A28
- DOI: https://doi.org/10.1090/S0002-9939-1979-0534403-0
- MathSciNet review: 534403